d dimensional SO(d)-Higgs Models with Instanton and Sphaleron: d=2,3

TL;DR

This paper investigates instanton and sphaleron solutions in d-dimensional SO(d)-Higgs models in 2 and 3 dimensions, analyzing their topological properties and flux configurations.

Contribution

It constructs sphaleron solutions, calculates their Chern-Simons charges, and explores noncontractible loops between topologically distinct vacua in these models.

Findings

Constructed sphaleron solutions in 2D and 3D models.

Calculated Chern-Simons charges for sphalerons.

Identified noncontractible loops with non-vanishing magnetic flux.

Abstract

The Abelian Higgs model and the Georgi-Glashow model in 2 and 3 Euclidean dimensions respectively, support both finite size instantons and sphalerons. The instantons are the familiar Nielsen-Oleson vortices and the 't Hooft-Polyakov monopole solutions respectively. We have constructed the sphaleron solutions and calculated the Chern-Simons charges N_cs for sphalerons of both models and have constructed two types of noncontractible loops between topologically distinct vacuua. In the 3 dimensional model, the sphaleron and the vacuua have zero magnetic and electric flux while the configurations on the loops have non vanishing magnetic flux.